A discrete-time hybrid control model with Borel state and action spaces is introduced. In this type of models, the dynamic of the system is composed by two sub-dynamics affecting the evolution of the state; one is of a standard-type that runs almost every time and another is of a special-type that is active under special circumstances. The controller is able to use two different type of actions, each of them is applied to each of the two sub-dynamics, and the activations of these sub-dynamics are possible according to an activation rule that can be handled by the controller. Along this talk we will show the optimality results regarding this type of models, in particular, we try to show (i) a characterisation of the value function as a solution of a functional equation, (ii) the existence of optimal policies, (iii) the introduction of the continuation region. This talk is based on some join works with Tomas Prieto-Rumeau, Jose-Luis Menaldi and Maurice Robin.